Not for Publication
Online Appendix For:
First Impressions Matter:
Signalling as a Source of Policy Dynamics
Stephen Hansen∗
Michael McMahon†
December 17, 2015
∗
†
Universitat Pompeu Fabra and Barcelona GSE.
University of Warwick, CEPR, CAGE (Warwick), CEP (LSE), CfM (LSE), and CAMA (ANU).
Contents
A Signalling with Many Periods
A.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.2 Solution algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B Strategic Voting
B.1 Theoretical effects of strategic voting . . . . . . . . . . . .
B.2 Estimation with strategic voting: a two-step methodology
B.3 Empirical Results: Strategic Voting and Robustness . . . .
B.4 Equilibrium effect of signalling to committee members . . .
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C Alternative Measures of Inflation Aversion
19
D Ex-ante Differences between Members
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E Other Sources of Voting Dynamics
E.1 Career Trajectory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.2 Reappointment driving the results . . . . . . . . . . . . . . . . . . . . . .
E.3 Concerns About The Committee Reputation . . . . . . . . . . . . . . . .
22
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24
25
F Alternative Structural Specifications
27
1
A
Signalling with Many Periods
The model presented in the main paper features policymakers serving for two periods,
which makes analyzing the signalling incentive particularly clean. In this section, we
consider whether our key theoretical predictions are robust to a model with T > 2
periods.
A.1
Model
For simplicity, we focus on a single policymaker with one of two types—θ = L or θ = H
where H > L. θ is drawn from a Bernoulli distribution with Pr [ θ = H ] = r and privately
observed by the banker at the beginning of the game. Then, in each period t = 1, . . . , T ,
the banker and public play the following subgame (identical to that in the main paper):
1. qt is observed by the banker and public.
2. ωt is drawn but not observed by any player.
3. The public forms πtE .
4. The banker draws a signal st ∼ N (ωt , σt2 ).
5. The banker chooses rt ∈ {0, 1}, which the public observes.
6. πt is observed by all players.
The equilibrium concept we use to solve the game is Perfect Bayesian Equilibrium.
θ̂t (rt−1 | ωt−1 , qt−1 , θ̂t−1 ) is the public’s belief that the banker is of type θ = H in
period t. In general, this depends on the additional information contained in rt−1 given
ωt−1 , qt−1 , and the prior belief θ̂t−1 (let θ̂0 = r). Moreover, let Vt (θ, θ̂t ) be the expected
continuation value for banker type θ from playing the game from period t onwards given
θ̂t , and ∆t+1 (θ, qt , θ̂t | ωt ) ≡ Vt+1 [θ, θ̂t+1 (0 | ωt , qt , θ̂t )] − Vt+1 [θ, θ̂t+1 (1 | ωt , qt , θ̂t )] be the
change in the period t + 1 continuation value from voting 0 rather than 1 in period t. As
in the main paper, bankers adopt cutoff voting rules each period that satisfy
Ct (θ, qt , θ̂t ) =
µ0 + θ[π(0, 0) − π(1, 0)] + δ∆t+1 (θ, qt , θ̂t | 0)
µ1 − θ[π(1, 1) − π(0, 1)] − δ∆t+1 (θ, qt , θ̂t | 1)
.
(A.1)
The first two terms in the numerator and denominator reflect the impact of rt on period
t policy while the last term reflects the impact on future expected utility from signalling.
The key then is to understand the behavior of the ∆t+1 terms since they determine how
the cutoff evolves over time.
As a first step, the following result is helpful in understanding signalling incentives.
2
Lemma 1 Given qt , period t expected utility for type H with reputation θ̂t is
ut (H, qt , θ̂t ) =
n
h
i
o
qt −l[π(1, 1)] − Pr rt = 0 θ = H, θ̂t , qt , ωt = 1 µ1 + (1 − θ̂t )Hyt (θ̂t , qt , 1) +
n
h
i
o
(1 − qt ) −l[π(1, 0)] + Pr rt = 0 θ = H, θ̂t , qt , ωt = 0 µ0 + (1 − θ̂t )Hyt (θ̂t , qt , 0)
(A.2)
and for type L is
ut (L, qt , θ̂t ) =
n
h
i
o
qt −l[π(1, 1)] − Pr rt = 0 θ = L, θ̂t , qt , ωt = 1 µ1 − θ̂t Lyt (θ̂t , qt , 1) +
n
h
i
o
(1 − qt ) −l[π(1, 0)] + Pr rt = 0 θ = L, θ̂t , qt , ωt = 0 µ0 − θ̂t Lyt (θ̂t , qt , 0)
(A.3)
where yt (θ̂t , qt , ωt ) is
io
i
h
n h
.
[π(0, ωt ) − π(1, ωt )] Pr rt = 0 θ = H, θ̂t , qt , ωt − Pr rt = 0 θ = L, θ̂t , qt , ωt
h i
Proof. Let Pr rt θ, θ̂t , qt , ωt be the probability that type θ with reputation θ̂t given
qt and ωt chooses rt . Expected utility is then
h
i

Pr rt = 0 θ, θ̂t , qt , 1 {−l[π(0, 1)] + θπ(0, 1)} −

n h
i
h
i
o 


 θπ(0, 1) Pr rt = 0 H, θ̂t , qt , 1 θ̂t + Pr rt = 0 L, θ̂t , qt , 1 (1 − θ̂t ) + 

+
h
i
qt 

Pr rt = 1 θ, θ̂t , qt , 1 {−l[π(1, 1)] + θπ(1, 1)} −



n h
i
h
i
o 
θπ(1, 1) Pr rt = 1 H, θ̂t , qt , 1 θ̂t + Pr rt = 1 L, θ̂t , qt , 1 (1 − θ̂t )

h
i

Pr rt = 0 θ, θ̂t , qt , 0 {−l[π(0, 1)] + θπ(0, 1)} −

n h
i
h
i
o 


 θπ(0, 1) Pr rt = 0 H, θ̂t , qt , 0 θ̂t + Pr rt = 0 L, θ̂t , qt , 0 (1 − θ̂t ) + 

h
i
(1 − qt ) 


Pr rt = 1 θ, θ̂t , qt , 0 {−l[π(1, 1)] + θπ(1, 1)} −



n h
i
h
i
o 
θπ(1, 1) Pr rt = 1 H, θ̂t , qt , 0 θ̂t + Pr rt = 1 L, θ̂t , qt , 0 (1 − θ̂t )

This expression can be simplified. First consider a type θ = H. Conditional on state
3
ωt = ω utility is
i
− Pr rt = 0 H, θ̂t , qt , ω l[π(0, ω)]+
n h
i
h
io
θπ(0, ω)(1 − θ̂t ) Pr rt = 0 H, θ̂t , qt , ω − Pr rt = 0 L, θ̂t , qt , ω
−
h
i
Pr rt = 1 H, θ̂t , qt , ω l[π(1, ω)]+
n h
i
h
io
θπ(1, ω)(1 − θ̂t ) Pr rt = 1 H, θ̂t , qt , ω − Pr rt = 1 L, θ̂t , qt , ω
=
h
i
− Pr rt = 0 H, θ̂t , qt , ω l[π(0, ω)]+
n h
i
h
io
θπ(0, ω)(1 − θ̂t ) Pr rt = 0 H, θ̂t , qt , ω − Pr rt = 0 L, θ̂t , qt , ω
−
h
i
Pr rt = 1 H, θ̂t , qt , ω l[π(1, ω)]+
n
h
i
h
io
θπ(1, ω)(1 − θ̂t ) 1 − Pr rt = 0 H, θ̂t , qt , ω − 1 + Pr rt = 0 L, θ̂t , qt , ω
h
Further simplification gives type θ = H utility as
i
h
i
− Pr rt = 0 θ = H, θ̂t , qt , ω l[π(0, ω)] − Pr rt = 1 θ = H, θ̂t , qt , ω l[π(1, ω)]+
io
i
h
n h
(1 − θ̂t )H[π(0, ω) − π(1, ω)] Pr rt = 0 θ = H, θ̂t , qt , ω − Pr rt = 0 θ = L, θ̂t , qt , ω
h
Similarly the utility for a type θ = L is
i
i
h
h
− Pr rt = 0 θ = L, θ̂t , qt , ω l[π(0, ω)] − Pr rt = 1 θ = L, θ̂t , qt , ω l[π(1, ω)]−
n h
i
h
io
θ̂t L[π(0, ω) − π(1, ω)] Pr rt = 0 θ = H, θ̂t , qt , ω − Pr rt = 0 θ = L, θ̂t , qt , ω
i
i
h
h
The result follows by plugging in Pr rt = 1 θ, θ̂t , qt , ω = 1 − Pr rt = 0 θ, θ̂t , qt , ω .
For ease of interpretation, the proposition expresses expected utility in terms of the
probabilities that different types vote for low rates. The first two terms in the curly
brackets of the above expressions relate to the expected loss from deviations of inflation
from target, while the third term (that in yt ) relates to the expected output gap. When
the inflation-tolerant type chooses low rates more often in equilibrium, yt is positive, which
means the inflation-tolerant (inflation-averse) type faces a positive (negative) expected
output gap. The logic is that the public forms rational expectations on period t inflation
by averaging the behavior of each type, which underestimates true inflation when the
actual type is θ = H and overestimates it when θ = L.
Our interest lies in the effect of θ̂t on utility since this will determine whether a banker
in period t−1 wants to increase or decrease his reputation for inflation tolerance in period
t. First, it appears directly as a linear term with coefficient −θyt (θ̂t , qt , ωt ) which decreases
4
utility as θ̂t increases. The interpretation is that as the weight the public puts on the
type’s being θ = H increases, the higher its inflation expectations and the lower is the
output gap, which is precisely the effect we emphasize in the main paper.
Second, θ̂t also appears indirectly in the probability the banker chooses rt = 0, an
effect that arises whenever Ct (θ, qt , θ̂t ) is not constant in θ̂t . This effect is subtle. Different
values of θ̂t influence by how much rt will affect θ̂t+1 . For example, when θ̂t is near 0
or 1, rt will have little impact on θ̂t+1 , while
if θ̂t is near 0.5 the iimpact will be larger.
h
If Ct (θ, qt , θ̂t ) increases in θ̂t —so that Pr rt = 0 θ = H, θ̂t , qt , ωt increases—there are
several effects on utility. In state 1 the expected loss of deviation of inflation from target
increases since the probability of the wrong decision goes up, while the reverse is true
in state 0. Moreover, when Ct (θ, qt , θ̂t ) changes at different rates for the two types, the
value of yt also changes.
In the two-period model of the main paper, these secondary effects are not present.
The reason is that in the last period T , types θ = H and θ = L use the cutoffs
CT (H) =
µ0 + L[π(0, 0) − π(1, 0)]
µ0 + H[π(0, 0) − π(1, 0)]
and CT (L) =
,
µ1 − H[π(1, 1) − π(0, 1)]
µ1 − L[π(1, 1) − π(0, 1)]
(A.4)
which do not depend on θ̂T . Thus one can unambiguously (negatively) sign the effect on
welfare of an increase in θ̂T , and in period T − 1 there is always an incentive to signal a
more inflation-averse type. In contrast, in all periods t = 1, . . . , T − 2 the banker must
consider the indirect effects of reputation as well. In general, Ct (θ, qt , θ̂t ) is not monotonic
in θ̂t as explained in the preceding, so unambiguously signing how welfare changes with
the indirect effects is not straightforward. The key question is whether these indirect
effects might ever provide an incentive to signal the inflation-tolerant type that is strong
enough to overturn the direct effect to signal the inflation-averse type.
A.2
Solution algorithm
Given the ambiguity of the indirect effects, we choose to solve the equilibrium computationally, and then examine its properties. To do so, we use the following backwardinduction algorithm. We assume qt is drawn uniformly from some discrete set Q.
1. For each type, compute CT (θ) from (A.4) and VT (θ, θ̂T ) by averaging uT (θ, qT , θ̂T )
over qT ∈ Q.1
2. For each period t = T − 1, . . . , 1:
(a) For each θ̂t = 0.01, 0.03, . . . , 0.99:
1
Since the game ends after period T , the continuation value is equivalent to the period T utility.
5
i. For each qt ∈ Q:
A. Solve for Ct (L, qt , θ̂t ) and Ct (H, qt , θ̂t ) from (A.1) given Vt+1 (θ, θ̂t+1 ).
B. Compute ut (θ, qt , θ̂t ).
C. Compute the expected value of Vt+1 (θ, θ̂t+1 ) with respect to θ̂t+1 given
Ct (θ, qt , θ̂t ) and the fact that beliefs must evolve according to Bayes’
rule. Denote the result V t+1 (θ, qt , θ̂t ).
D. Compute Vt (θ, qt , θ̂t ) = ut (θ, qt , θ̂t ) + δV t+1 (θ, qt , θ̂t ).
(b) Approximate Ct (L, qt , θ̂t ) and Ct (H, qt , θ̂t ) for all values θ̂t ∈ [0, 1] by fitting a
five-degree polynomial through the points computed in point A above.
(c) Compute Vt (θ, θ̂t ) by averaging over Vt (θ, qt , θ̂t ) from step D above. Then
approximate Vt (θ, θ̂t ) for all values θ̂t ∈ [0, 1] by fitting a five-degree polynomial
through the computed values.
We approximate the equilibrium cutoffs and value functions due to the following. Given
Ct (θ, qt , θ̂t ), one can compute the exact values for θ̂t+1 at which to compute the value
function Vt+1 . But because Ct (θ, qt , θ̂t ) depends on Vt+1 their values are determined
jointly in equilibrium. For this reason, we approximate Vt+1 at all values of θ̂t+1 in order
to facilitate computation of Ct (θ, qt , θ̂t ).
We compute the equilibrium at the following values:2
1. T = 36. This corresponds to the number of meetings in the average term on the
MPC. In the below we refer to a time period as a month.
2. δ = 0.998. This corresponds to the discount factor given a real annual interest rate
of 0.03, the typical value in our sample.
3. Realized inflation. This is consistent with hitting the inflation target when matching
the interest rate to the state, and symmetric deviations otherwise.
(a) π(0, 0) = 2
(b) π(1, 0) = 1.9
(c) π(1, 1) = 2
(d) π(0, 1) = 2.1
4. Loss function. This is consistent with treating upside and downside misses equivalently. It is larger than that implied by a quadratic loss in order to ensure both
banker types wish to match the decision to the state.
2
We use R for the exercise, in particular its nleqslv package. We achieve convergence at point A in
the algorithm above in every loop.
6
(a) µ0 = 0.06
(b) µ1 = 0.06
5. Types L = 0.3 and H = 0.5. These ensure that the more inflation-averse type
places less weight on the output gap. The levels, though higher than the weight for
the Federal Reserve used in Woodford (2003), are within the range in Debortoli,
Kim, Linde, and Nunes (2015) for the estimated (0.25) and the optimal (1) weight
placed on the output gap.
6. σt = 0.4 in every period. This is the value we estimate in the data.
7. Q is the set of 137 fitted values for qt from the main paper.
A.3
Results
Our primary question of interest is whether our theoretical results on the evolution of
equilibrium cutoffs hold period-by-period. In order to focus on the extent to which time
alone is responsible for changing signalling incentives, we explore how Ct (θ, qt , θ̂t ) behaves
holding fixed qt and θ̂t . In other words, we ask whether for all qt+1 = qt ∈ Q, θ̂t+1 = θ̂t ∈
[0, 1] we have that
1. Ct+1 (θ, qt , θ̂t ) > Ct (θ, qt , θ̂t ) for each type.
h
i h
i
2. Ct+1 (H, qt , θ̂t ) − Ct (H, qt , θ̂t ) − Ct+1 (L, qt , θ̂t ) − Ct (L, qt , θ̂t ) > 0.
To get an idea of why one might expect this to hold, recall that the shape of the value
function determines the direction and strength of the signalling incentive. Figures A.1a
and A.1b plot the value function for each type at 36 months (the last period of the game)
and at 18 months (the middle of the game). In both periods, the continuation value of
the game is declining in reputation (recall this is the belief the public puts on the banker’s
having type θ = H). This means that in periods 35 and 17 both types have an incentive
to signal type θ = L. But the rate at which the continuation value changes in period
18 is substantially higher than the rate in period 36. Figures A.1c and A.1d plot the
marginal valuations of signalling the more inflation-averse type (decreasing θ̂t ) at 36 and
18 months. Clearly, the marginal value is substantially higher in the middle of the game
than at the end. Finally, in each period the inflation tolerant type θ = H has a higher
marginal valuation of improving its reputation. As in the main paper, the intuition is it
cares more about building a reputation since it weights the output gap more.
To further illustrate these features of the equilibrium, table A.1 provides the estimated
coefficients of the constant and linear term of the polynomial approximation for the value
functions at different points in time. Focusing on the linear term, again one finds the
7
0.44
0.36
0.016
0.38
0.018
0.40
0.020
0.42
0.022
0.024
Type L
Type H
0.0
0.2
0.4
0.6
0.8
1.0
0.0
0.2
Reputation
0.4
0.6
0.8
1.0
Reputation
(b) Continuation Value at 18 Months
0.25
0.006
(a) Continuation Value at 36 Months
Type L
Type H
0.00
0.000
0.001
0.05
0.002
0.10
0.003
0.15
0.004
0.20
0.005
Type L
Type H
0.0
0.2
0.4
0.6
0.8
1.0
0.0
Reputation
0.2
0.4
0.6
0.8
1.0
Reputation
(c) Marginal Absolute Value at 36 Months
(d) Marginal Absolute Value at 18 Months
Figure A.1: Continuation Values over Time for Two Types
Notes: The top row of this figure plots approximated values of the value functions V36 (θ, θ̂36 )
and V18 (θ, θ̂18 ) for each type. The bottom row plots the absolute value of the derivatives
of these functions with respect to θ̂t . Note that each subfigure is drawn on a different scale
on the vertical axis.
8
same basic pattern. In each period it is negative, its absolute value decreases over time,
and its absolute value is higher for the inflation-tolerant type.
Table A.1: Approximations of Value Functions at Different Periods
T
36 Months
30 Months
24 Months
18 Months
12 Months
6 Months
Constant
θ=L θ=H
0.02
0.02
0.16
0.16
0.29
0.30
0.43
0.44
0.56
0.58
0.69
0.71
Linear
θ=L
-0.002
-0.016
-0.030
-0.047
-0.067
-0.088
Term
θ=H
-0.004
-0.032
-0.068
-0.108
-0.150
-0.193
Given this evidence, it should be unsurprising that we find that the two inequalities
above indeed hold for all Q and for every value of reputation θ̂t we have examined, 0.01
through 0.99 in increments of 0.01. In this sense, we are confident that our basic logic
from the two-period model is robust to the introduction of multiple periods. Another
way of interpreting this result is that the indirect effects in the T -period model are less
quantitatively important than the direct effect we focus on in the main paper.
We should also note that the main effect of signalling comes in the initial periods of the
game since this is when changes in θ̂t have the highest marginal impact on continuation
values. The marginal impact then declines steadily over time before becoming relatively
small in the later stages of the game. For example, the linear term at 36 months in table
A.1 induces a signalling incentive in period 35 that is many times smaller than the linear
term at 6 months induces in period 5. In this sense, the equilibrium does not feature
notable end-game effects in which there is some discontinuous shift in behavior in moving
to the last period.
9
B
Strategic Voting
In the main text, both the model and the empirical analysis were based on the assumption
of sincere voting behavior. This section explores the theoretical effects and empirical
implications of strategic, i.e. pivotal, voting.
B.1
Theoretical effects of strategic voting
In line with Duggan and Martinelli (2001), we focus on responsive equilibria in which all
members have a positive probability of voting for high and low rates. The main difference
with the sincere case is that members now condition their votes on changing the outcome,
or being pivotal. Let E { Pr [ PIVit | ωt ] | p−it } be the expected probability that member
i’s vote is pivotal in period t given ωt and his colleagues’ reputations p−it (the expectation
is taken with respect to other members’ types). This is the expected probability of all
the events in which exactly N2−1 of his colleagues vote for high rates, and N2−1 vote for
low rates. In responsive equilibria, these probabilities are all non-zero. We modify the
definition of cutoff voting rules slightly to be those in which member i chooses vit = 1 if
and only if
ω
bit E { Pr [ PIVit | 1 ] | p−it }
≥ CitST R ,
1−ω
bit E { Pr [ PIVit | 0 ] | p−it }
where CitST R is i’s period t cutoff under strategic voting. In line with lemma 1 in the main
R
text, member i equivalently chooses vit = 1 if and only if sit ≥ sST
CitST R , σit , qt , p−it
it
where
qt
E
{ Pr [ PIVit | 1 ] | p−it }
1
2
ST R
ST R
+ ln
(B.1)
sit (·) ≡ − σit ln
2
1 − qt
E{ Pr [ PIVit | 0 ] | p−it } − ln Cit
is the threshold i’s signal must reach to induce him to vote high. An equilibrium of the
model is a set of N thresholds such that (B.1) holds for each member i.
An important difference with the sincere case is that voting behavior now depends on
colleagues’ reputations. This is because the probability of being pivotal depends on the
probability that colleagues vote high, which in turn depends on their preference types
about which i has beliefs p−it . Hence rookie votes now indirectly affect others’ future
voting behavior, so strategic voting introduces an additional signalling channel absent in
the sincere model.
This new effect is difficult to characterize outside of special cases because of the large
number of pivotal events and general distribution of types. For this reason, we view the
question of whether and how voting depends on colleagues’ reputations as an empirical
question. To explore it, for each member i in each meeting t, we generate an index
of the voting behavior of his veteran colleagues when they were rookies. The variable
10
ColleaguePit is defined as the fraction of votes that all veterans on the period t MPC cast
when rookies that were high (excluding member i in the case he is a veteran). We then
estimate the regression
vit = µi + δt + λColleaguePit + it ,
(B.2)
with results reported in table B.2. We find no evidence that a member is any more or
less likely to vote for high rates when his veteran colleagues have established a reputation
for inflation aversion. This might be because members simply do not vote strategically,
or because pivot probabilities do not change markedly with p−it . The rest of this section
makes the latter assumption, and ignores the dependence of pivot probabilities on p−it .
Table B.2: Effect of inflation-averse colleagues on own voting behavior
(1)
vit
Main Regressors
ColleaguePit
-0.0049
[0.658]
1.21*
[0.082]
Constant
Number of mem num
R-squared
Model
Member effects?
Time effects?
Sample?
Obs?
26
0.674
Panel LPM
YES
YES
12/98-03/09
1106
Notes: This regression presents OLS estimates of equation B.2. Standard errors clustered
by member. The dependent variable, vit , is our measure of whether member i votes for the
high interest rate in period t. The results show that, controlling for member and time fixed
effects, whether other existing members have voted for high rates more in the past has no
effect on the probability that a given member votes for high rates.
The analogue of veterans’ utility from choosing vit expressed in the proof of proposition
1 is3
UV (vit , θi ) = ω
bit {−l [π(vit , 1)] + θi π(vit , 1)} Pr [ PIVit | 1 ]+
(1 − ω
bit ) {−l [π(vit , 0)] + θi π(vit , 0)} Pr [ PIVit | 0 ] − θi πtE .
from which one obtains the voting rule of choosing vit = 1 if and only if
ω
bit Pr [ PIVit | 1 ]
µ0 + θi [π(0, 0) − π(1, 0)]
≥
≡ CVST R (θi ),
1−ω
bit Pr [ PIVit | 0 ]
µ1 − θi [π(0, 1) − π(1, 1)]
3
(B.3)
For the rest of this section, we drop the expectations with respect to p−it in the pivot probabilities
in line with the empirical finding in table B.2.
11
where CVST R (θi ) is the veteran’s cutoff under strategic voting.
For rookies, the expected utility from choosing vit is
UR (vit , θi ) = ω
bit {−l [π(vit , 1)] + θi π(vit , 1)} Pr [ PIVit | 1 ] +
(1 − ω
bit ) {−l [π(vit , 0)] + θi π(vit , 0)} Pr [ PIVit | 0 ] − θi πtE −
R
R
+ vit , qt , NtR , qt+1 , Nt+1
, ωt+1
.
δθi E π E∗ p V−it
Re-writing this expression gives a cutoff voting rule with cutoff
CRST R θi , qt , NtR ≡
µ0 + θi [π(0, 0) − π(1, 0)] − ∆(qt , NtR | 0)/ Pr [ PIVit | 0 ]
.
µ1 − θi {[π(0, 1) − π(1, 1)] − ∆(qt , NtR | 1)/ Pr [ PIVit | 1 ]}
(B.4)
where ∆(qt , NtR | ωt ) is as defined in the main text.
As in the sincere model discussed in the main text, the probability that veterans and
rookies vote low is increasing in type, so a low vote by rookie i in period t leads the public
to associate i with a higher θi and to increase its belief on the probability i will vote low
in period t + 1 when a veteran (for formal details see the proof of proposition 2). So ∆
continues to be positive and the two empirical predictions in the main text hold.
B.2
Estimation with strategic voting: a two-step methodology
In this section we describe how to estimate the model under strategic voting using the
two-step estimator of Iaryczower and Shum (2012). For convenience, we begin by rewriting the likelihood function from the main text:
#
"
Y
t
qt
Y
(κ1it )vit (1 − κ1it )1−vit + (1 − qt )
i
Y
(κ0it )vit (1 − κ0it )1−vit ,
(B.5)
i
where
κ1it ≡ 1 − Φ
s∗it (·) − 1
σi
and κ0it ≡ 1 − Φ
s∗it (·)
σi
.
(B.6)
κ0it (κ1it ) is the probability member i in meeting t votes high conditional on ωt = 0
(ωt = 1), and qt and (1 − qt ) are the prior probabilities that the economy is in the high
and low inflation states, respectively. Under strategic voting, s∗it (·) is a function of all
other members’ thresholds since these enter the probability of being pivotal by equation
(B.1).4 For this reason, directly maximizing (B.5) with respect to cutoffs and expertise
is no longer feasible.
The basic idea of the two-step estimator is the following:
4
This is true even without any dependence of the pivot probabilities on p−it .
12
1. Specify κ0it and κ1it with flexible functional forms that depend on observed covariates. These functions are not linked to any particular economic model. This yields
the estimated values for voting probabilities κ
b0it and κ
b1it .
2. The second step links to the economic model by backing structural parameters
out of the equilibrium equations that generate κ
b0it and κ
b1it . Here one can assume
either sincere or strategic voting for the equilibrium equations. For completeness,
we present both sincere and strategic results, thus providing a robustness check on
the sincere estimates in the main text from the direct approach.
Specifically, the model for the prior is:
exp α0 + α1 qtR + α2 qtM
,
qt =
1 + exp (α0 + α1 qtR + α2 qtM )
(B.7)
where qtR and qtM are proxy variables used in the main text. The models for the κ terms
are:
exp (β · Xit )
κ0it + exp (γ · Xit )
κ0it =
and κ1it =
(B.8)
1 + exp (β · Xit )
1 + exp (γ · Xit )
where Xit is a vector of covariates. For the baseline specification, we use
Xit = 1, qtR , qtM , D(Int)i , D(Vet)it , D(N R )t , D(Hike)t , D(Int)i · qtR , D(Int)i · qtM .
These are the same covariates as used in the main text with the addition of the interactions
between D(Int)i and the proxies for the prior, which control for members’ with different
signal precisions reacting differently to changes in the prior. To test the difference-indifferences prediction, we use
Xit =
1, qtR , qtM , D(Int)i , D(Vet)it , D(N R )t , D(Hike)t , D(Int)i · qtR ,
D(Int)i · qtM , D(θP CT Exp )i , D(θP CT Exp )i · D(Vet)it
!
,
where D(θP CT Exp )i is defined as in the main text.5
The dependence of κ1 on κ0 ensures that κ1 ≥ κ0 , which is implied by the model and
necessary for identifying the first stage parameters β and γ. Without the restriction that
κ1 ≥ κ0 , assigning individual votes to the cluster corresponding to the correct inflationary
state is not possible. We estimate the α, β, and γ via maximum likelihood applied to
(B.5), and obtain fitted values qbt , κ
b0it , and κ
b1it .
For the second step, with either sincere or strategic voting, one can use (B.6) to
5
We present results for just D(θP CT Exp )i to save on space, results for D(θP CT )i are similar.
13
recover estimates of sb∗it and σit with the following equations:
sb∗it
1
Φ−1 (1 − κ
b0it )
and σ
bit = −1
.
= −1
−1
Φ (1 − κ
b0it ) + Φ (b
κ1it )
Φ (1 − κ
b0it ) − Φ−1 (1 − κ
b1it )
(B.9)
Obtaining estimates for the cutoff Cit requires specifying the sincere or strategic model.
bit can be obtained by plugging qbt , σ
Under the former, C
bit , and sb∗it into the equation (2)
in the main text and solving directly.
[ PIVit | 1 ]
Under strategic voting, for each member i we first compute an estimate of Pr
Pr [ PIVit | 0 ]
in the following way. From the estimates of κ
b0jt and κ
b1jt for j 6= i, one can compute the
probability that exactly N2−1 of i’s colleagues vote high in states 0 and 1, respectively.
(Note that conditional on the state ωt , the probability that members vote high is iid).
bitST R as
We then use the empirical analogue of (B.1) to back out C

∗
sit − 1
bST R = exp  2b
C
+ ln
it
2b
σit2
qbt
1 − qbt
i 
d
Pr PIVit 1
i  .
+ ln  h
d
Pr PIVit 0

h
bit and
By construction, the two-step approach delivers separate estimates of σ
bit , C
bitST R for each meeting (or more precisely, for each value of qbt , which is different for every
C
meeting). Testing our empirical predictions therefore requires comparing distributions of
estimated parameters. To test empirical prediction 1 using the baseline specification, we
bit and C
bST R by rookie and veteran
report the median of the estimated values of σ
bit , C
it
separately. We prefer the median to the mean to avoid having the results driven by tail
values of the estimated parameters. To test empirical prediction 2 using the expanded
set of covariates, we report the median separately by rookie and veteran, and by inflation
averse and inflation tolerant.6
B.3
Empirical Results: Strategic Voting and Robustness
Table B.3 provides the results for empirical prediction 1. These are equivalent to the
results which are presented in table 2 in main text, and the evolution of cutoffs from
that table is replicated on the first line of table B.3. The second line, marked “C 2step Sincere”, shows the evolution of the cutoffs if we continue to assume members vote
6
Confidence intervals are constructed using the same approach in Hansen, McMahon, and Velasco
(2014). This involves a Monte-Carlo approach that is similar in spirit to boot-strapping. We make
1,000 draws of first-stage coefficients from a multivariate normal distribution centered on the vector of
estimated coefficients with variance-covariance matrix that is the inverse of the negative Hessian matrix.
For each draw, we generate an estimate for the value of the expertise and cutoff parameters exactly as
in the second stage of estimation (by computing different values for each meeting from the equilibrium
equations, and then taking the median value across meetings). This generates a simulated distribution
of structural parameter estimates (and their differences) that we use to construct confidence intervals.
14
sincerely but use the two-step methodology. Then the third line reports the results
assuming members vote strategically (“C 2-step Strategic”). The qualitative results are
unchanged in each case, though the average level of the C tends to be lower under
the assumption of strategic voting. Using the two-step methodology, expertise changes
modestly with tenure. However, rather than learning through their tenure, the average
member appears to become less expert with tenure.
Table B.3: Baseline Results: Robustness to strategic voting
C(θ) Baseline (Sincere, direct)
C(θ) 2-step Sincere
C(θ) 2-step Strategic
σ 2-step
Baseline
Rookie Veteran Difference
0.87
3.17
2.30
[0.003]
0.29
1.42
1.13
[0.000]
0.15
0.56
0.41
[0.000]
0.38
0.42
0.04
[0.097]
Notes: This table reports the estimated cutoffs for the average MPC member. As in the
main text, the final column compares the effect of experience on the increase in the cutoff
between the two groups. The terms reported in brackets are p-values, calculated using a
bootstrapped distribution of estimates, for a one-sided test of difference from zero.
Table B.4 provides the results for empirical prediction 2 (table 3 in main text). The
difference-in-differences results are also qualitatively unaffected by the two-step methodology or the assumption of strategic voting.
Table B.4: Difference in Differences Results: Robustness to strategic voting using
D(θP CT Exp )i
C(θ) Baseline (Sincere, direct)
C(θ) 2-step Sincere
C(θ) 2-step Strategic
Inflation Averse
Rookie Veteran Difference
0.33
1.58
1.26
[0.007]
0.10
1.20
1.09
[0.000]
0.03
0.17
0.14
[0.040]
Inflation Tolerant
Rookie Veteran Difference
1.52
11.22
9.69
[0.006]
0.62
4.75
4.13
[0.000]
0.03
0.48
0.45
[0.001]
Diff-in-Diff
-8.43
[0.008]
-3.03
[0.001]
-0.31
[0.018]
Notes: This table reports the estimated cutoffs for high and low θi types based on the
D(θP CT Exp )i measure. As in the main text, the final column compares the effect of experience on the increase in the cutoff between the two groups. The terms reported in brackets
are p-values, calculated using a bootstrapped distribution of estimates, for a one-sided test
of difference from zero.
B.4
Equilibrium effect of signalling to committee members
Above we argue that the same qualitative predictions from the sincere voting model
carry over to the strategic voting model when the effect of signalling to one’s colleagues
15
is small. This assumption is consistent with the voting data insofar as, according to
table B.2, the marginal effect of one’s colleagues voting more hawkishly in the past
(and therefore signalling a lower type) on current voting behavior is insignificant. We
now analyze whether the assumption is also consistent with an actual equilibrium of the
strategic voting game played at the values of the structural parameters we estimate and
present in table B.4.
To do so, we consider a two-period model and nine-person committee in which all
members are rookies in the first period and veterans in the second. This is equivalent to
the model in the main paper with N1 = 9 and N0 = 0. We choose this environment to
isolate the effect of the secondary signalling effect without adding the complication of how
it might vary over the particular composition of rookies and veterans on the committee.
For simplicity we assume there are two types in the population θ = L and θ = H where
L < H. Let θ̂it be the belief that the public attaches to member i’s having type H. We
assume that θ̂i1 = 0.5 for all i so that ex ante types have equal probability. θ̂i2 takes one
of two values depending on whether i votes low or high in the first period. Let Ĥ (L̂)
be the reputation that follows from voting low (high) in period 1. In any equilibrium we
must have that Ĥ > L̂.
We begin by considering the equilibrium in the second period in which all members are
veterans. Since rookies use symmetric strategies, we can replace p−i2 with the number of
colleagues who voted high in period 1, or x−i . This depends on the total number of high
votes from the first period xH as well as member i’s vote vi1 . When vi1 = 0, x−i = xH ,
and when vi2 = 1, x−i = xH − 1. We denote an equilibrium threshold in the second
period for member i as s∗2 (θi , vi1 , xH , L̂, Ĥ). There are four such objects corresponding to
the two types and two possible first period votes. It is important to keep in mind that
the values of L̂ and Ĥ are endogenous quantities generated by the equilibrium of the first
period and are independent of the realized value of xH . Our basic question of interest is
the effect of xH on second period voting behavior.
Adapting equation (B.1) to this specific setup, we obtain
s∗2 (θi , vi1 , xH , L̂, Ĥ) ≡
o

 n

E
Pr
[
PIV
|
1
]
v
,
x
,
L̂,
Ĥ
i1
H
q2
1
o  − ln C2ST R (θi )  .
− σ22 ln
+ ln  n
2
1 − q2
E Pr [ PIV | 0 ] vi1, xH , L̂, Ĥ
(B.10)
We use structural parameters estimated from the data and presented in tables B.3 and
B.4: σ2 = 0.42, C2ST R (L) = 0.17, and C2ST R (H) = 0.48. Given q2 , one can then solve the
16
four-by-four system of equations that (B.10) represents.7
The impact of xH on second period voting depends on L̂ and Ĥ. Suppose as a
thought experiment that L̂ = Ĥ. In this case, the number of voters who vote high in
period 1 is uninformative about the type distribution in the population since different
votes do not lead to different posterior beliefs on type. On the other hand, as Ĥ grows
larger relative to L̂, xH becomes more informative about the composition of types on the
second period committee. This in turn changes the computation of the pivot probabilities
and potentially the equilibrium. By how much is the question we seek to answer.
Taken at face value, the estimates presented in table B.4 are consistent with there
being little separation in equilibrium between different types, and therefore little difference between L̂ and Ĥ. One must go to the third decimal place to find a difference in
cutoffs. To bias our results in favor of there being effects on period 2 voting behavior
from changes in xH , we instead assume that type θ = L (θ = H) adopts a rookie cutoff
given by the 25th (75th) percentile of the distribution generated by bootstrapping, or
C1ST R (L) = 0.013 (C1ST R (H) = 0.084). An equilibrium of the first period is then given by
s∗1 (θi )
ST R
q1
E
{ Pr [ PIV | 1 ] }
1
2
+ ln
≡ − σ1 ln
2
1 − q1
E{ Pr [ PIV | 0 ] } − ln C1 (θi) ,
(B.11)
where the expectation for the pivot probabilities is computed using the common uniform
prior distribution on types. (B.11) represents a two-by-two system of equations that one
can again solve numerically. Given ω1 , one can then obtain by Bayes’ Rule the following
expressions:
h
s∗1 (H)−ω1
σ1
i
Φ
Pr [ vi1 = 0 | θi = H, ω1 ] Pr [ θi = H ]
i
h ∗
i
= h ∗
s1 (H)−ω1
s1 (L)−ω1
Pr
[
v
=
0
|
θ
=
x,
ω
]
Pr
[
θ
=
x
]
i1
i
1
i
x∈{L,H}
Φ
+Φ
σ1
σ1
h ∗
i
s1 (H)−ω1
1
−
Φ
σ1
Pr [ vi1 = 1 | θi = H, ω1 ] Pr [ θi = H ]
h ∗
i
h ∗
i.
L̂ = P
=
s (H)−ω1
s (L)−ω1
x∈{L,H} Pr [ vi1 = 1 | θi = x, ω1 ] Pr [ θi = x ]
1−Φ 1
+1−Φ 1
Ĥ = P
σ1
σ1
Given these equilibrium strategies and belief updates, we conduct a simulation exercise
by repeating the following 1,000 times:
1. Draw q1 from one of the 137 fitted values (with replacement) from the structural
exercise presented in table B.4.
2. Compute s∗1 (θi ) from (B.11).
3. Draw ω1 given q1 .
7
We obtain solutions using the nleqslv package in R.
17
4. Compute L̂ and Ĥ as above.
5. Draw q2 from one of the 137 fitted values (with replacement).
6. Compute s∗2 (θi , vi1 , xH , L̂, Ĥ) for xH = 1, . . . , 8 from (B.10).8
7. Draw ω2 given q2 .
8. Compute the average marginal effect of changes in xH on the probability of voting
high in period 2 as
7
1 X
7
xH =1
(
"
s∗ (θi , vi1 , xH + 1, L̂, Ĥ) − ω2
1−Φ 2
σ2
#) (
"
s∗ (θi , vi1 , xH , L̂, Ĥ) − ω2
− 1−Φ 2
σ2
#)
.
We express the impact of xH on second period voting probabilities rather than thresholds since their values are easier to interpret empirically. In the language of the current
setup, a member’s voting high rather than low in period 1 increases the value of xH by
1; the quantity computed in part 8 of the simulation is the average marginal impact of
increasing xH on the probability that colleagues vote high. Our assumption above is that
this reaction is small in magnitude. Moreover, the average reaction in the data to an
increase in ColleaguePit as reported in table B.2 is insignificant, with a point estimate of
−0.0049 and a 95% confidence interval of (-0.0274, 0.0176).
Table B.5: Marginal effects of number of high votes in period 1 on probability of high
vote in period 2
θi = L,vi1 = 0
θi = H,vi1 = 0
θi = L,vi1 = 1
θi = H,vi1 = 1
Mean Median
0.0060 0.0055
0.0062 0.0067
0.0060 0.0044
0.0058 0.0057
Minimum Maximum
0.0029
0.0111
0.0026
0.0109
0.0018
0.0117
0.0038
0.0103
Table B.5 presents the mean, median, minimum, and maximum values of this quantity
across the 1,000 draws of the simulation for each of the four possible equilibrium strategies
played in the second period. In each case, the mean and median reactions are around half
a percentage point, thus essentially the same in absolute value as the estimated coefficient
on ColleaguePit . Moreover, the maximum values are slightly above one percentage point,
well within the confidence interval for the estimated coefficient. Thus we conclude that
the assumption that players do not react meaningfully to others’ earlier votes is consistent
with equilibrium behavior.
8
We exclude from the equilibrium computations situations in which xH = 0 or xH = 9 since in these
cases there is only one equilibrium cutoff for each type, and the four-by-four system in (B.10) collapses
to a two-by-two system. We can solve such a system, but prefer to remain in the four-by-four case for
consistency.
18
C
Alternative Measures of Inflation Aversion
As described in the robustness section in the main paper, we augment the difference-indifferences analysis by using two alternative ways of measuring inflation aversion. The
first alternative comes from Eijffinger, Mahieu, and Raes (2013), which we call EMR
hereafter. They rank members along a policy space of interest rates, and so identify
members that systematically prefer higher or lower rates. We rank members based on
the reported ideal points in EMR, and create an indicator variable D(θEM R )i for inflation
tolerance that roughly splits the sample equally based on this ranking.
We also use the estimated fixed effects from the regression in table 1 in the main paper
to define an indicator variable D(θF E )i . Members with higher fixed effects are assigned
D(θF E )i = 0 and those a lower fixed effects are assigned a 0. We split the sample evenly.
These fixed effects capture average voting tendencies while controlling for common factors
driving voting behavior within a given meeting due to the inclusion of time fixed effects.
Table C.6 shows that the reduced form analysis using different measures of risk aversion continues to give a mixed picture of the difference-in-differences prediction.
Table C.6: Reduced-form evidence using different measures of inflation aversion
Main Regressors
D(Vet)
D(θP CT Exp ) x D(Vet)
(1)
vit
(2)
vit
(3)
vit
(4)
vit
-0.031
[0.351]
-0.13***
[0.003]
-0.038
[0.314]
-0.100***
[0.004]
-0.099***
[0.005]
D(θP CT ) x D(Vet)
-0.080*
[0.055]
D(θEM R ) x D(Vet)
0.018
[0.674]
D(θF E ) x D(Vet)
Constant
R-squared
Model
Member effects?
Time effects?
Sample?
Obs?
1.22***
[0.000]
0.95***
[0.000]
0.707
0.705
Panel LPM Panel LPM
YES
YES
YES
YES
06/97-03/09 06/97-03/09
1204
1246
0.98***
[0.000]
0.014
[0.731]
0.98***
[0.000]
0.704
Panel LPM
YES
YES
06/97-03/09
1246
0.704
Panel LPM
YES
YES
06/97-03/09
1246
Notes: This regression presents OLS estimates of equation (7) in the main paper with
standard errors clustered by member. The dependent variable, vit , is our measure of
whether member i votes for the high interest rate in period t.
Table C.7 presents the structural estimates for all four measures we use in the paper.
The difference-in-differences prediction remains robust to these alternative approaches to
19
measuring inflation aversion.
Table C.7: Robustness of the structural difference in differences estimates
D(θP CT Exp )
Inflation Averse
Rookie Veteran Difference
0.47
2.87
2.40
[0.000]
Inflation Tolerant
Rookie Veteran Difference
1.88
16.83
14.95
[0.000]
Diff-in-Diff
-12.55
[0.000]
D(θP CT )
0.30
0.68
0.38
[0.048]
2.45
18.28
15.84
[0.000]
-15.46
[0.000]
D(θEM R )
0.27
1.13
0.86
[0.000]
5.02
20.59
15.57
[0.010]
-14.71
[0.015]
D(θF E )
0.09
0.85
0.76
[0.000]
5.33
15.05
9.72
[0.018]
-8.95
[0.022]
Notes: This regression presents structural estimates of cutoff by type of member measured
in four different ways. The results show that our main structural estimates are robust
across other measures of member type.
20
D
Ex-ante Differences between Members
Table D.8 presents the results of table 3 in the main paper separately for internal and
external members. The main difference-in-differences prediction—that all members become more dovish but especially the more inflation-tolerant members—holds conditional
on appointment type. This allays potential concerns that internal and external members
behave very differently in the data.
Table D.8: Dynamic behaviour of different member types conditional on appointment
Baseline
C(θ)
Internal
C(θ)
External C(θ)
Baseline
C(θ)
Internal
C(θ)
External C(θ)
Inflation Averse
D(θ P CT Exp ) = 0
Rookie Veteran Difference
0.47
2.87
2.40
[0.000]
0.11
0.75
0.63
[0.000]
0.89
4.34
3.45
[0.000]
Inflation Averse
D(θ P CT ) = 0
Rookie Veteran Difference
0.30
0.68
0.38
[0.048]
0.05
0.17
0.12
[0.007]
0.53
1.88
1.35
[0.006]
Inflation Tolerant
D(θ P CT Exp ) = 1
Rookie Veteran Difference
1.88
16.83
14.95
[0.000]
0.42
2.11
1.69
[0.000]
1.77
12.69
10.92
[0.000]
Inflation Tolerant
D(θ P CT ) = 1
Rookie Veteran Difference
2.45
18.28
15.84
[0.000]
0.49
3.93
3.44
[0.000]
3.79
36.04
32.26
[0.000]
Diff-in-Diff
-12.55
[0.000]
-1.06
[0.012]
-7.47
[0.004]
Diff-in-Diff
-15.46
[0.000]
-3.32
[0.000]
-30.90
[0.000]
Notes: This table reports the results of table 3 in the main paper separately for internal
and external members. The difference-in-differences prediction holds for each appointment
status.
21
E
Other Sources of Voting Dynamics
In this section we further consider three alternative sources of voting dynamics, briefly
mentioned in section 2.3 of the main text, besides the desire to signal one’s preference
type. The first is that members change their cutoffs to pursue particular career paths,
the second is that their behaviour is driven by a desire for reappointment, and the third
is that they care about the reputation of the committee as a whole rather than their
personal reputations.
E.1
Career Trajectory
As an example of how pursuing a particular career path might drive the results, suppose
that MPC members wishing to work in the private sector after leaving the committee
became softer on inflation over time in order to signal to future employers their friendliness
towards business.9 Then our finding of overall increasing cutoffs might be driven solely by
this group becoming softer on inflation over time, while others’ cutoff remained constant.
To analyze this idea, we examine four different splits of the committee. The first
two are whether members came from an academic or private-sector background prior to
joining the MPC, while the last two are whether members went to an academic or privatesector position after leaving the MPC. Table E.9 summarises these career variables for
each member of our sample.
We use the following specifications for the cutoff and expertise:
ln (Cit ) = β0 +β1 ·D(Vet)it +β2 ·D(N R )t +β3 ·D(Int)i +β4 ·D(Hike)t +β5 ·D(Career)i (E.1)
and
ln (σit ) = γ0 + γ1 · D(Vet)it + γ2 · D(Int)i + γ3 · D(Career)i ,
(E.2)
where D(Career)i is one of the four career variables. We then estimate the β and γ
coefficients (along with coefficients for equation (10) that specifies qt ), and back out
values for Cit and σit as described in section 5.1. Their average values by veteran status
and career trajectory are reported in table E.10.
All subgroups have a significant increase in their estimated cutoff. Thus while particular groups might increase more than others, there is a common tendency to become
more dovish that is independent of one’s career trajectory. It is worth pointing out that
whenever one group is estimated as substantially more inflation tolerant than another, as
is the case for all splits except post-MPC academic, that group also has a larger estimated
move in the cutoff. This is consistent with the difference-in-differences prediction, but
9
One fact that already makes this story somewhat less compelling is the absence of an end of term
effect in the data (see section 4 of the main text for details).
22
Table E.9: Career Covariates for MPC Members in Our Sample
Member
Davies
George
King
Plenderleith
Clementi
Vickers
Bean
Tucker
Large
Lomax
Gieve
Dale
Fisher
D(Int)i
Internal
Internal
Internal
Internal
Internal
Internal
Internal
Internal
Internal
Internal
Internal
Internal
Internal
First
Meeting
Jun 1997
Jun 1997
Jun 1997
Jun 1997
Sep 1997
Jun 1998
Oct 2000
Jun 2002
Oct 2002
Jul 2003
Feb 2006
Jul 2008
Mar 2009
Last
Meeting
Jul 1997
Jun 2003
Pre-MPC Career
Academic Private
0
0
0
0
0
0
May 2002
0
0
Aug 2002
0
1
Sep 2000
1
0
1
0
0
0
Jan 2006
0
0
Jun 2008
0
0
Feb 2009
0
0
0
0
0
0
Buiter
Goodhart
Julius
Budd
Wadhwani
Allsop
Nickell
Barker
Bell
Lambert
Walton
Blanchflower
Besley
Sentence
External
External
External
External
External
External
External
External
External
External
External
External
External
External
Jun 1997
Jun 1997
Sep 1997
Dec 1997
Jun 1999
Jun 2000
Jun 2000
Jun 2001
Jul 2002
Jun 2003
Jul 2005
Jun 2006
Sep 2006
Oct 2006
May
May
May
May
May
May
May
2000
2000
2001
1999
2002
2003
2006
Jun 2005
Mar 2006
Jun 2006
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
Post-MPC Career
Academic Private
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
Notes: This table provides the career covariates for the MPC members in our sample.
Those with missing values in the “Last Meeting” column were still sitting on the MPC in
March 2009, the month our sample ends. All such members have since left the MPC, so
that there are no missing values for the Post-MPC Career variables.
23
could also be driven by other differences between groups besides the weight put on the
output gap. Overall, the results in the main paper do not appear driven by any particular
group seeking out specific career goals.
Table E.10: Career Effects
Pre-MPC
Non-Private Sector
Rookie Veteran Difference
0.58
2.39
1.81
[0.000]
Private Sector
Rookie Veteran Difference
1.92
7.61
5.69
[0.000]
C(θ)
Post-MPC
Pre-MPC
0.83
2.68
1.86
[0.000]
Non-Academic
Rookie Veteran Difference
0.79
2.39
1.60
[0.000]
1.17
6.86
5.69
[0.000]
Academic
Rookie Veteran Difference
1.13
6.14
5.01
[0.000]
C(θ)
Post-MPC
0.87
3.63
2.77
[0.000]
0.92
3.00
2.08
[0.000]
Notes: This table examines the evolution of cutoffs by different types of career covariate.
All career splits experience a similar increase in cutoff.
E.2
Reappointment driving the results
As discussed in the main text, all members of the committee (both internal and external),
apart from Governor-level positions, serve three-year terms; Governors and Deputy Governors serve five-year terms. However, reappointment is possible. It is therefore feasible
that reappointment incentives drive the behaviour of MPC members. In particular, it
would be worrying for our interpretation of the empirical findings if members became
more dovish toward the end of their first term in order to be reappointed. To do this we
examine the relationship between the type proxies and reappointment, and show that, if
anything, more hawkish (internal) members are more likely to be reappointed to serve a
second term.
To do this, we define a dummy variable for each member, D(Reappointed)i , which is
equal to 1 if member i served a second term (without distinguishing whether the person
wanted to serve a second term or not). We then estimate a linear probability model:
D(Reappointed)i = µ + δ0 D(External)i + δ1 D(θX )i + δ1 D(θX )i × D(Vet)it + it
(E.3)
where D(θX )i is one of our type proxies.
Table E.11 presents the results. They show that, if anything, more hawkish internal
members are more likely to be reappointed (column (1)). Of course, for these regressions
24
Table E.11: Reduced-form evidence on the drivers of reappointment to second term
Main Regressors
D(External)
D(θP CT Exp ) x D(External)
(1)
D(Reappointed)i
(2)
D(Reappointed)i
(3)
D(Reappointed)i
0.042
[0.889]
0.069
[0.879]
-0.095
[0.724]
-0.26
[0.341]
D(θP CT ) x D(External)
-0.11
[0.763]
D(θEM R ) x D(External)
D(θP CT Exp )
0.18
[0.638]
-0.62*
[0.087]
D(θP CT )
-0.095
[0.724]
D(θEM R )
Constant
R-squared
Model
Member effects?
Time effects?
Sample?
Obs?
0.62***
[0.001]
0.43**
[0.026]
-0.095
[0.727]
0.43**
[0.028]
0.326
OLS
NO
NO
06/97-03/09
22
0.066
OLS
NO
NO
06/97-03/09
27
0.044
OLS
NO
NO
06/97-03/09
27
Notes: This regression presents OLS estimates of a linear probability model in which the
dependent variable is a dummy equal to 1 if member i was reappointed after the end of
their first term.
there is at most one observation per member, and the D(θP CT Exp )i has only 22 members
with non-missing observations. This means that the statistical power of the regression is
low. So while not conclusive evidence against any changes in behavior driven by a desire
to be reappointed, these findings at least reassure us that a desire to be seen as a dove
to increase chances of reappointment are not the main drivers of the dynamic behavior
we discuss in the main paper.
E.3
Concerns About The Committee Reputation
As we discuss in section 2.3 of the main text, while not entirely straightforward to microfound, members might care about the reputation of the committee as a whole in addition
to their individual reputations. In this section we explore whether such concerns are the
main driver of our results. If members in the sample cared about the reputation of the
MPC for inflation aversion, they should have been particularly motivated to establish its
credibility during its initial meetings when there was the most uncertainty about how it
25
would operate. Moreover, since those serving during the first meetings were by definition
rookies, this group may be responsible for our empirical finding that rookies are tougher
on inflation than veterans.
If this story were true, then removing the rookie votes from the first 18 meetings from
the structural exercise should lead to a much less marked difference in the cutoff between
veterans and rookies. In table E.12, we present results from repeating the structural
estimation of the cutoffs reported in section 5.2 of the main text, but dropping from the
sample any meeting between June 1997 and December 1998 (the first 18 months).10 The
top panel of the table shows that there remains a significant increase in the estimated
cutoff on average. The lower panels show the estimates for different levels of θi (identified
using the D(θP CT Exp )i measure) as well as the difference-in-differences estimate. Again,
the main results of the paper are unaffected; all types have a significant increase in their
cutoffs, but the increase is significantly greater for more inflation-tolerant members.
These results show that individual reputations matter in the sense that even after
the MPC matured as an institution, rookies continued to use significantly higher cutoffs
than veterans overall, and especially when they were more inflation tolerant. This does
not imply that committee reputation concerns are not present in the data, just that they
alone do not appear able to explain the empirical results.
Table E.12: Estimates of cutoffs excluding the first 18 months of the MPC
C(θ)
Baseline
Rookie
1.64
Veteran
5.04
Difference
3.40
[0.000]
Inflation Averse
0.44
2.34
Inflation Tolerant
3.32
19.07
1.90
[0.001]
15.74
[0.000]
-13.84
[0.002]
Diff-in-Diff
Notes: This table shows the structural estimates of the cutoffs (C) for rookies and veteran
members, as well as the difference between them. We report, in brackets below the difference
estimate, the p-value of a one-sided test that the difference is significantly non-zero; the
test is calculated using a bootstrapped distribution of estimates. The first panel shows the
estimates for the overall average on the committee. The second panel reports the estimated
cutoffs for high and low θi types based on the high vote percentage measure. The final panel
reports the difference-in-differences estimate between the high and low θi types.
10
We have also done this for the reduced form analysis in section 4 and the results are unaffected.
26
F
Alternative Structural Specifications
Finally, we conduct a number of checks on the robustness of the specification used for
the structural analysis. In the baseline specification, the three equations estimated in the
structural model are:
qt
= α0 + α1 · qtR + α2 · qtM
(F.1)
ln
1 − qt
ln (Cit ) = β0 + β1 · D(Vet)it + β2 · D(N R )t + β3 · D(Int)i + β4 · D(Hike)t
(F.2)
ln (σit ) = γ0 + γ1 · D(Vet)it + γ2 · D(Int)i
(F.3)
where D(N R )t indicates whether the period t committee composition includes at least
three rookies, D(Int)i indicates whether member i is internal, and D(Hike)t indicates
whether the agenda includes at least one option to raise rates.
Our first robustness check uses a more flexible specification for equation (F.3) in which
we allow the expertise to vary with the agenda by including the D(Hike)t variable:
ln (σit ) = γ0 + γ1 · D(Vet)it + γ2 · D(Int)i + γ3 · D(Hike)t
(F.4)
The baseline results, as well as those under the more flexible specfication for σ, are
shown in Table F.13. The evolution of both C(θ) and σ is very similar.
Table F.13: Estimates of cutoffs under an alternative specification for σ
C(θ)
Baseline
Rookie
0.84
Veteran
3.07
Difference
2.23
[0.000]
Inflation Averse
0.42
2.46
Inflation Tolerant
1.70
15.12
2.04
[0.000]
13.43
[0.000]
-11.39
[0.000]
Diff-in-Diff
Notes: This table shows the structural estimates of the cutoffs (C) for rookies (column 1)
and veteran (column 2) members, as well as the difference between them (column 3). We
report, in brackets below the difference estimate, the p-value of a one-sided test that the
difference is significantly non-zero; the test is calculated using a bootstrapped distribution
of estimates. The first panel shows the estimates for the overall average on the committee.
The second panel reports the estimated cutoffs for high and low D(θP CT Exp )i types based
on the high vote percentage measure. The final panel reports the difference-in-differences
estimate between the high and low D(θP CT Exp )i types.
Next we include only the terms predicted by our model, D(Vet)it and D(N R )t , in
27
equation (F.2) and otherwise leave the baseline specification as it is.
ln (Cit ) = β0 + β1 · D(Vet)it + β2 · D(N R )t
(F.5)
Again, the results, shown in F.14, support the idea that our results are robust to a
more parsimonious specification.
Table F.14: Estimates of cutoffs using a more parsimonious specification for cutoffs
C(θ)
Baseline
Rookie
2.77
Veteran
4.15
Difference
1.37
[0.080]
Inflation Averse
1.53
3.12
Inflation Tolerant
4.98
19.40
1.59
[0.024]
14.42
[0.005]
-12.83
[0.009]
Diff-in-Diff
Notes: This table shows the structural estimates of the cutoffs (C) for rookies and veteran
members, as well as the difference between them. We report, in brackets below the difference
estimate, the p-value of a one-sided test that the difference is significantly non-zero; the
test is calculated using a bootstrapped distribution of estimates. The first panel shows the
estimates for the overall average on the committee. The second panel reports the estimated
cutoffs for high and low D(θP CT Exp )i types based on the high vote percentage measure.
The final panel reports the difference-in-differences estimate between the high and low
D(θP CT Exp )i types.
Finally, since Mervyn King was present at all the committee meetings in the sample,
he arguably does not truly fit our model’s assumption. We therefore re-estimate the
structural parameters using the same specification as in the main paper, but dropping all
of this votes. F.15 displays the results, which are qualitatively equivalent to those that
include King.
28
Table F.15: Estimates of cutoffs excluding Mervyn King from the sample
C(θ)
Baseline
Rookie
1.13
Veteran
5.50
Difference
4.37
[0.000]
Inflation Averse
0.47
2.87
Inflation Tolerant
1.88
16.83
2.40
[0.000]
14.95
[0.000]
-12.55
[0.000]
Diff-in-Diff
Notes: This table shows the structural estimates of the cutoffs (C) for rookies and veteran
members, as well as the difference between them. We report, in brackets below the difference
estimate, the p-value of a one-sided test that the difference is significantly non-zero; the
test is calculated using a bootstrapped distribution of estimates. The first panel shows the
estimates for the overall average on the committee. The second panel reports the estimated
cutoffs for high and low D(θP CT Exp )i types based on the high vote percentage measure.
The final panel reports the difference-in-differences estimate between the high and low
D(θP CT Exp )i types.
References
Debortoli, D., J. Kim, J. Linde, and R. Nunes (2015): “Designing a simple loss
function for the Fed: does the dual mandate make sense?,” Working Papers 15-3,
Federal Reserve Bank of Boston.
Duggan, J., and C. Martinelli (2001): “A Bayesian Model of Voting in Juries,”
Games and Economic Behavior, 37(2), 259–294.
Eijffinger, S. C. W., R. J. Mahieu, and L. Raes (2013): “Inferring Hawks and
Doves from Voting Records,” Discussion Paper DP9418, CEPR.
Hansen, S., M. McMahon, and C. Velasco (2014): “How Experts Decide: Preferences or Private Assessments on a Monetary Policy Committee?,” Journal of Monetary
Economics, 67(October), 16–32.
Iaryczower, M., and M. Shum (2012): “The Value of Information in the Court: Get
It Right, Keep It Tight,” American Economic Review, 102(1), 202–37.
Woodford, M. (2003): Interest and Prices. Princeton University Press.
29